Communication is an important capability for multi-robot exploration because (1) inter-robot communication (comms) improves coverage efficiency and (2) robot-to-base comms improves situational awareness. Exploring comms-restricted (e.g., subterranean) environments requires a multi-robot system to tolerate and anticipate intermittent connectivity, and to carefully consider comms requirements, otherwise mission-critical data may be lost. In this paper, we describe and analyze ACHORD (Autonomous & Collaborative High-Bandwidth Operations with Radio Droppables), a multi-layer networking solution which tightly co-designs the network architecture and high-level decision-making for improved comms. ACHORD provides bandwidth prioritization and timely and reliable data transfer despite intermittent connectivity. Furthermore, it exposes low-layer networking metrics to the application layer to enable robots to autonomously monitor, map, and extend the network via droppable radios, as well as restore connectivity to improve collaborative exploration. We evaluate our solution with respect to the comms performance in several challenging underground environments including the DARPA SubT Finals competition environment. Our findings support the use of data stratification and flow control to improve bandwidth-usage.